Flow Boundaries in Random-Flight Dispersion Models: Enforcing the Well-Mixed Condition

Abstract

Lagrangian stochastic (LS) dispersion models often use trajectory reflection to limit the domain accessible to a particle. It is shown how the well-mixed condition (Thomson) can he expressed in the Chapman-Kolmogorov equation for a discrete-time LS model to provide a test for the validity of a reflection algorithm. By that means it is shown that the usual algorithm (perfect reflection) is exactly consistent with the wmc when used to bound Gaussian homogeneous turbulence, but that no reflection scheme can satisfy the wmc when applied at a location where the probability distribution for the normal velocity is asymmetric, or locally inhomogeneous. Thus, there is no well-mixed reflection scheme for inhomogeneous or skew turbulence.